Check out the Shared cM chart to see the possibilities relationship around 1148 cM. It could be half niece/nephrew, niece/nephrew, great-niece/nephew, grandchild, and so on. You have to use genealogy to confirm the relationship. You do this by starting with the birth year of the match. Then try to fit them into your tree to confirm the relationship.
My concern is for the emotional toll this is taking on you. When dealing with an unexpected result, it's important to take time to process and confide your feelings into someone you trust. If the idea of being his half-aunt is not something you are excited about, it may be that you just aren't ready to process more information right now. Your dad will always be your dad who raised you. Make sure you are ready to deal with the good and bad consequences before you start to get to know your bio-dad's family. Remember that your mental health is most important. Follow your heart.